A note on cascade flux laws for the stochastically-driven nonlinear Schrödinger equation

IF 1.6 2区数学 Q2 MATHEMATICS, APPLIED

Nonlinearity Pub Date : 2024-04-21 DOI:10.1088/1361-6544/ad3794

Jacob Bedrossian

引用次数: 0

Abstract

In this note we point out some simple sufficient (plausible) conditions for ‘turbulence’ cascades in suitable limits of damped, stochastically-driven nonlinear Schrödinger equation in a d-dimensional periodic box. Simple characterizations of dissipation anomalies for the wave action and kinetic energy in rough analogy with those that arise for fully developed turbulence in the 2D Navier–Stokes equations are given and sufficient conditions are given which differentiate between a ‘weak’ turbulence regime and a ‘strong’ turbulence regime. The proofs are relatively straightforward once the statements are identified, but we hope that it might be useful for thinking about mathematically precise formulations of the statistically-stationary wave turbulence problem.

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关于随机驱动非线性薛定谔方程的级联通量定律的说明

在本论文中，我们指出了在 d 维周期箱中阻尼随机驱动非线性薛定谔方程的适当极限中 "湍流 "级联的一些简单充分（可信）条件。我们给出了波作用和动能耗散异常的简单特征，与二维纳维-斯托克斯方程中充分发展的湍流所产生的特征进行了大致类比，并给出了区分 "弱 "湍流机制和 "强 "湍流机制的充分条件。一旦确定了语句，证明就相对简单了，但我们希望这可能有助于思考统计静止波湍流问题的数学精确表述。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Nonlinearity 物理-物理：数学物理

CiteScore

3.00

自引率

5.90%

发文量

170

审稿时长

12 months

期刊介绍： Aimed primarily at mathematicians and physicists interested in research on nonlinear phenomena, the journal''s coverage ranges from proofs of important theorems to papers presenting ideas, conjectures and numerical or physical experiments of significant physical and mathematical interest. Subject coverage: The journal publishes papers on nonlinear mathematics, mathematical physics, experimental physics, theoretical physics and other areas in the sciences where nonlinear phenomena are of fundamental importance. A more detailed indication is given by the subject interests of the Editorial Board members, which are listed in every issue of the journal. Due to the broad scope of Nonlinearity, and in order to make all papers published in the journal accessible to its wide readership, authors are required to provide sufficient introductory material in their paper. This material should contain enough detail and background information to place their research into context and to make it understandable to scientists working on nonlinear phenomena. Nonlinearity is a journal of the Institute of Physics and the London Mathematical Society.